Which physicist developed wave mechanics and published its central equation in 1926?

Erwin Schrödinger developed wave mechanics and published its central equation in 1926.

Schrödinger introduced his wave equation in a series of papers during 1926. The time-dependent Schrödinger equation describes how a nonrelativistic quantum state changes, while the time-independent form is used to find allowed energy states in systems such as atoms and harmonic oscillators. His approach represented quantum states with wavefunctions rather than matrix quantities.

The wavefunction itself is not normally interpreted as a directly measurable wave of matter. Max Born later supplied the standard probabilistic interpretation, in which the squared magnitude of the wavefunction gives a probability density. Schrödinger shared the 1933 Nobel Prize in Physics with Paul Dirac. His famous 1935 cat thought experiment was intended to highlight problems in interpreting quantum superposition, not to describe an actual macroscopic cat experiment.